Problem: Ishaan is 28 years younger than Umaima. Twelve years ago, Umaima was 5 times older than Ishaan. How old is Umaima now?
Explanation: We can use the given information to write down two equations that describe the ages of Umaima and Ishaan. Let Umaima's current age be $u$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $u = i + 28$ Twelve years ago, Umaima was $u - 12$ years old, and Ishaan was $i - 12$ years old. The information in the second sentence can be expressed in the following equation: $u - 12 = 5(i - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to solve our first equation for $i$ and substitute it into our second equation. Solving our first equation for $i$ , we get: $i = u - 28$ . Substituting this into our second equation, we get the equation: $u - 12 = 5($ $(u - 28)$ $ -$ $ 12)$ which combines the information about $u$ from both of our original equations. Simplifying the right side of this equation, we get: $u - 12 = 5u - 200$ Solving for $u$ , we get: $4 u = 188$ $u = 47$.